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          <h1 class="post-title" itemprop="name headline">PAT B1035/A1089</h1>
        

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        <p>According to Wikipedia:</p>
<p>Insertion sort iterates, consuming one input element each repetition, and growing a sorted output list. Each iteration, insertion sort removes one element from the input data, finds the location it belongs within the sorted list, and inserts it there. It repeats until no input elements remain.</p>
<p>Merge sort works as follows: Divide the unsorted list into N sublists, each containing 1 element (a list of 1 element is considered sorted). Then repeatedly merge two adjacent sublists to produce new sorted sublists until there is only 1 sublist remaining.</p>
<p>Now given the initial sequence of integers, together with a sequence which is a result of several iterations of some sorting method, can you tell which sorting method we are using?</p>
<p>Input Specification:</p>
<p>Each input file contains one test case. For each case, the first line gives a positive integer N (&lt;=100). Then in the next line, N integers are given as the initial sequence. The last line contains the partially sorted sequence of the N numbers. It is assumed that the target sequence is always ascending. All the numbers in a line are separated by a space.</p>
<p>Output Specification:</p>
<p>For each test case, print in the first line either “Insertion Sort” or “Merge Sort” to indicate the method used to obtain the partial result. Then run this method for one more iteration and output in the second line the resulting sequence. It is guaranteed that the answer is unique for each test case. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.</p>
<p>Sample Input 1:<br>10<br>3 1 2 8 7 5 9 4 6 0<br>1 2 3 7 8 5 9 4 6 0<br>Sample Output 1:<br>Insertion Sort<br>1 2 3 5 7 8 9 4 6 0<br>Sample Input 2:<br>10<br>3 1 2 8 7 5 9 4 0 6<br>1 3 2 8 5 7 4 9 0 6<br>Sample Output 2:<br>Merge Sort<br>1 2 3 8 4 5 7 9 0 6<br><figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br></pre></td><td class="code"><pre><span class="line">#include &quot;stdio.h&quot;</span><br><span class="line">//#include &quot;math.h&quot;</span><br><span class="line">//#include &quot;string.h&quot;</span><br><span class="line">//#include &quot;iostream&quot;</span><br><span class="line">#include &quot;algorithm&quot;</span><br><span class="line">using namespace std;</span><br><span class="line">const int N = 110;</span><br><span class="line">int origin[N], tempOri[N], changed[N];</span><br><span class="line">int n;//元素个数</span><br><span class="line">bool isSame(int A[], int B[])&#123;</span><br><span class="line">    for (int i = 0; i &lt; n; i++) &#123;</span><br><span class="line">        if (A[i] != B[i]) return false;</span><br><span class="line">    &#125;</span><br><span class="line">    return true;</span><br><span class="line">&#125;</span><br><span class="line">void showArray(int A[])&#123;</span><br><span class="line">    for (int i = 0; i &lt; n; i++) &#123;</span><br><span class="line">        printf(&quot;%d&quot;, A[i]);</span><br><span class="line">        if (i &lt; n - 1) printf(&quot; &quot;);</span><br><span class="line">    &#125;</span><br><span class="line">    printf(&quot;\n&quot;);</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line">bool insertSort()&#123;</span><br><span class="line">    bool flag = false;//记录是否存在数组中间步骤与changed数组相同</span><br><span class="line">    for (int i = 1; i &lt; n; i++) &#123;</span><br><span class="line">        if (i != 1 &amp;&amp; isSame(tempOri, changed)) &#123;</span><br><span class="line">            flag = true;</span><br><span class="line">        &#125;</span><br><span class="line">        int temp = tempOri[i], j = i;</span><br><span class="line">        while (j &gt; 0 &amp;&amp; tempOri[j - 1] &gt; temp) &#123;</span><br><span class="line">            tempOri[j] = tempOri[j - 1];</span><br><span class="line">            j--;</span><br><span class="line">        &#125;</span><br><span class="line">        tempOri[j] = temp;</span><br><span class="line">        if (flag == true) &#123;</span><br><span class="line">            return true;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    return false;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line">void mergeSort()&#123;</span><br><span class="line">    bool flag = false;</span><br><span class="line">    for (int step = 2; step / 2 &lt; n; step *=2) &#123;</span><br><span class="line">        if (step != 2 &amp;&amp; isSame(tempOri, changed)) &#123;</span><br><span class="line">            flag = true;</span><br><span class="line">        &#125;</span><br><span class="line">        for (int i = 0; i &lt; n; i += step) &#123;</span><br><span class="line">            sort(tempOri + i, tempOri + min(i + step, n));</span><br><span class="line">        &#125;</span><br><span class="line">        if (flag == true) &#123;</span><br><span class="line">            return;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    </span><br><span class="line">&#125;</span><br><span class="line">int main()&#123;</span><br><span class="line">    scanf(&quot;%d&quot;, &amp;n);</span><br><span class="line">    for (int i = 0; i &lt; n ; i++) &#123;</span><br><span class="line">        scanf(&quot;%d&quot;, &amp;origin[i]);</span><br><span class="line">        tempOri[i] = origin[i];</span><br><span class="line">    &#125;</span><br><span class="line">    for (int i = 0; i &lt; n; i++) &#123;</span><br><span class="line">        scanf(&quot;%d&quot;, &amp;changed[i]);</span><br><span class="line">    &#125;</span><br><span class="line">    if (insertSort()) &#123;</span><br><span class="line">        printf(&quot;Insertion Sort\n&quot;);</span><br><span class="line">        showArray(tempOri);</span><br><span class="line">    &#125;else&#123;</span><br><span class="line">        printf(&quot;Merge Sort\n&quot;);</span><br><span class="line">        for (int i = 0; i &lt; n; i++) &#123;</span><br><span class="line">            tempOri[i] = origin[i];</span><br><span class="line">        &#125;</span><br><span class="line">        mergeSort();</span><br><span class="line">        showArray(tempOri);</span><br><span class="line">    &#125;</span><br><span class="line">    return 0;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure></p>
<p>陷阱：<br>原始序列不参与是否与目标序列相同的比较<br>给定下列样例测试<br>//input<br>4<br>3 4 2 1<br>3 4 2 1<br>//output<br>Inertion Sort<br>2 3 4 1</p>
<p>2017年02月24日补充：<br>此题类似<a href="http://blog.hemisu.com/archives/220/" target="_blank" rel="noopener">A1098</a></p>

      
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